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http://s27.postimg.org/m6mecvwgz/pro_1117.pngPer the result of problem 368 we haveB3C3 is an angle bisector of ∠ (AB3B1) => A4 is incenter of triangle AB1B3And B1A4 is an angle bisector of ∠( AB1B3)Per the result of problems 1114 and 1116 we have 60 degrees angles and 30 degrees angles as shown on the attached sketch ( see sketch )So ∠ (A4B1B2)= ∠ (B1B2A1) = 30 degrees => B1A4//A1B2Similarly we will have C1B2// B1C4